We didn't always live in a world where vast conspiracies simmered in our collective consciousness, fuelled by provocative explanations. In 1996 Gary Webb, an investigative journalist with California's San Jose Mercury News, published a series of reports that alleged a connection between the Central Intelligence Agency and drug smuggling into the United States undertaken by anti-Communist rebels they were working with in Nicaragua. Webb's reporting made headlines but was then undercut and denied. There were no truthers to ignite back then.

A reporter becomes the target of a life-threatening smear campaign after he exposes the CIA's role in arming Contra rebels in Nicaragua and importing cocaine to the US. Based on a true story.

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Webb's rise and part of his fall is the subject of Kill the Messenger, a drama about media ethics and official culpability that ultimately plays out much like the subject matter Webb was trying to capture with his writing: it stays just out of reach. Michael Cuesta's movie, notable for a fine lead performance by Jeremy Renner as Webb, is capable and suggestive but it never attains definitive proof.

Like many stories of unlikely investigations and revelations of wrongdoing, the film has a good feel for the act of conversion required to get past the initial disbelief and the tension that accumulates. For Webb it starts with Coral (Paz Vega), the girlfriend of a cocaine trafficker about to go on trial. She tells him her boyfriend has been charged by one arm of the US government for work previously approved by another in the 1980s.

The trail soon leads to a cocaine kingpin who brought enough powder into the US to fuel the nightmarish crack epidemic that was concentrated in the nation's African-American communities. With his journalistic antenna up, and the mood growing brisk and uneasy, Webb is soon in Latin America conversing with lawyers, visiting airstrips and meeting a sanguine crime lord, Norwin Meneses (Andy Garcia), who treats his jail like a personal fiefdom.

Webb is confident, sometimes cavalier. He lives in the suburbs with his wife Sue (Rosemarie DeWitt) and three children, and he pursues the story not for personal glory but because he believes revealing the truth is vital. If he's excited by what he finds, he's equally rattled by the blowback he receives, particularly the succession of sombre men in suits who begin to populate his life, and then his imagination.

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In other words, Webb is no superhero, which is a welcome change for Renner, who plays one – the bow-and-arrow-wielding Hawkeye – in various Marvel movies including The Avengers. This has been a breakthrough 12 months for the American actor, whose intensity in Kathryn Bigelow's The Hurt Locker in 2008 was subsequently in danger of calcifying into something blunt and monomaniacal.

In American Hustle, Kill the Messenger and, particularly, The Immigrant, Renner has revealed a freewheeling quality that has shaded easy readings of his characters. The flaws of the men he plays are now mercurial, and you can sense the pain Webb feels when the acclaim he initially receives turns to scorn.

Marking the spot: Jeremy Renner as US journalist Gary Webb in Kill the Messenger.

Unlike Alan J Pakula's 1976 Watergate procedural film All the President's Men, this is not a film that treats the wider newspaper field with reverence. Webb's expose riled the major American papers and their star national security reporters, who worked harder to poke holes in his reporting than to corroborate it, eventually leading Webb's editors, Jerry Ceppos (Oliver Platt) and Anna Simons (Mary Elizabeth Winstead, fast becoming an exceptional character actor), to publicly rescind some of his conclusions.

"I think we overreached," the real Jerry Ceppos recently told The New York Times, but the film never really gets into the minutiae of what's alleged and what can be verified. That shortage of detail is something of a flaw in the film, which shoehorns in scenes such as Webb briefly walking through a crack-ridden LA housing project in a bid to to apply perspective to what he is doing.

On the wall: Jeremy Renner as journalist Gary Webb in a scene from Kill the Messenger.

The direction by Cuesta, a former independent filmmaker who has spent the past decade in television, most notably on Homeland, is concise and in the moment: in tracking shots the camera falls back as Webb strides towards it, staying just out of reach as you study Renner's clouded features. But the story never digs in quite deep enough, as if it's afraid of muddying a sad if understandable outline.

Webb got some vindication in a US Congressional report in 1998, but it was ignored in the furore over President Clinton's relationship with Monica Lewinsky. Kill the Messenger ends with Webb's bittersweet departure from the San Jose Mercury News in 1997, segmenting off his life story in an unappealing way given that the film's subject was someone who, for better and ultimately much worse, committed everything.